THE COSMIC RAY FLUX IN TIME

In meteorites, short-term cosmic ray flux variations can be recognized by measuring the activity of a radionuclide with a short half-life in meteorites with a known fall date. Longer-term variations are studied by comparing apparent production rates of stable (noble gas) nuclides based on various pairs of a stable and a radioactive nuclide, or by comparing experimental and model data (see Production systematics subsection). 

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The above models are all rather unsatisfactory, because they involve somewhat arbitrary assumptions about the time-dependence of the cosmic-ray flux and spectrum and because they predict a secondary-like behaviour for Be and B abundances, whereas the overall trend indicated by the data is more like a primary one and there are the energetic difficulties pointed out above. In the case of nB, there is a possible primary mechanism for stellar production in supemovae by neutrino spallation processes (Woosley et al. 1990 Woosley Weaver 1995), but the primary-like behaviour of beryllium in metal-poor stars, combined with a constant B/Be ratio of about 20 fully consistent with cosmic-ray spallation (Garcia Lopez et al. 1998) in the absence of any known similar process for Be, indicates that this does not solve the problem unless a primary process can be found for Be as well. Indeed,... 

Secondary cosmic ray flux and cosmic ray composition at the Earth s surface are complex quantities to evaluate, and in practice assumptions about the constancy of cosmic rays over timescales relevant to paleoaltimetry research. Short time scale variations in production rates, such as might result from the 11-year cyclicity in the cosmic ray flux due to solar flares (Raisbeck et al. 1990), will average out of the data over million-year timescales. Likewise, assumptions about the constancy of atmospheric density must be made so that atmospheric depth can be converted to elevation. 

C-14 dating was discovered by Libby11 and co-worker [2], The cosmic ray flux has been fairly constant over prehistoric and current time and provides a small but almost constant supply of 6C14, at a rate averaged over the whole atmosphere of about 2.2 atoms cm-2 s 1. The radioactive 6C14 will bind to oxygen in the atmosphere to form radioactive carbon dioxide, but will decay, with a half-life fi/2 = 5730 years, by emitting an electron (or "fj ray") and an electron antineutrino ... 

The related unresolved issue concerns the prevalence of multiple exposures. For example, Lavielle et al. (1999) identify Bendego as an iron that may have undergone multiple periods of exposure, presumably initiated by collisions, and there are others such as Canyon Diablo (Michlovich et al., 1994). In general, we would expect collisions to reduce the sizes of meteoroids and thereby increase production rates, i.e., to have the same qualitative effect as would an increase in the cosmic-ray flux. Such changes, however, should change production rates at random times and by random increments. The relative importance of multiple exposures in irons is difficult to assess from the available data. 

If it can be assumed that the rate of production has not varied over time, and thus that a dynamic equilibrium has formed, and if it is possible to extract clean sample carbon, unaltered apart from the decline in and to measure its current concentration, it is possible using eqn [1] to calculate the elapsed time since the death of the organism. In practice, the process is far more complicated than this brief description indicates. Principally, one of the basic assumptions, that the rate of formation is constant, is known to be incorrect. The rate has, in fact, varied over time in response to a number of effects, principally fluctuations in the cosmic-ray flux with changes in the geomagnetic field and in solar activity. Because of this, no radiocarbon measurement equates directly with a calendar date, and all such measurements must be calibrated before use. 

A fundamental assumption made for most dating with atmospheric radionuclides is that the cosmic radiation flux and hence, the natural production of the radionuclides has been constant with time. Various studies of this problem using 14C and tree-ring calibration have been made. Isotopic studies of meteorites have also been useful [17]. Considering the probable lack of basic accuracy of dating water, the problem of changes in cosmic ray flux is not serious. 

Reedy RC, Marti M (1991) Solar-cosmic ray fluxes during the last ten million years. In The Sun in time. 

For some radionuclides, only the direct measurement is needed, based on calibration with a radionuclide standard and reference to the measured sample mass. For other radionuclides, the isotope ratio to its stable element is needed. An example of a more complex situation is measurement of the 14C/12C isotope ratio of an environmental or archeological sample in comparison to the modern atmospheric CO2 value. This value must be adjusted for anthropogenic 14C produced by atmospheric testing of nuclear weapons and by other nuclear operations, and also for changes in atmospheric CO2 with cosmic-ray flux fluctuations over time. For an element such as Pu, which has no stable isotope, the total quantity is measured by isotope dilution mass spectrometry in which the sample is traced (or spiked) with 242Pu or 244Pu (see Section 17.3.3). 

When Fritz Paneth s group in 1953 tried to determine meteorite ages by the He/U method (Paneth et al. 1953), they found much larger amounts of helium than could be accounted for by uranium decay and thus stumbled on the discovery of cosmic-ray-induced nuclear reactions in meteorites that subsequently became the subject of extensive research. Many radionuclides with half-lives ranging from days to millions of years as well as some stable spallation products have been identified in meteorites. From the amounts found, the exposure ages of meteorites in space and the average cosmic-ray flux and its time variation can be deduced (see, e.g., Schaeffer 1968). 

It is germane to add that the observed content of He in meteorites has been used to determine their H/ He age and the method involved dividing the recorded total number of He atoms by the number of He atoms decaying per unit time and making a 30% correction for the directly produced He. Results were dubious in part because of the need to assume that there was a constant He content or a constant cosmic-ray flux at the meteoroid integrated over 25 years. 

In Table 7.2, we summarize major He fluxes in the atmosphere. The He budget seems to be in balance, at least within a factor of two, although there is certainly room for modification of some of the terms or introduction of new ones. However, there is no reason to require the He budget to be in balance. On the 106 year scale of the mean residence time, variations in fluxes will be smoothed out, and the present epoch may not be typical. The geological and cosmic ray sources are probably fairly steady on this time scale, but the thermal loss is very sensitive to solar activity, the nonthermal loss is sensitive to the geomagnetic field, and precipitation is sensitive to both. At an extreme, the fluxes may be highly irregular Sheldon and Kern (1972),... 

For a constant flux of galactic cosmic rays (for further discussion of this point, see LavieUe et al. (1999)), the time dependence vanishes. The parameters, size and depth, remain along with the elemental abundances and nuclear cross-sections in principle, the elemental abundances and nuclear cross-sections can be measured directly. 

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